Question

Determine whether the function is even, odd, or neither. Discuss the

symmetries of the graphs.

f(x)=x^4–2x^2

Any help would be appreciated. Thanks!

Answer 1

• even
• symmetrical about the y-axis

Explanation:

You know the function is even because all the terms in its definition have even degree.

An even function is one that satisfies ...

f(x) = f(-x)

An even power of -x is the same as that power of x. (-x)^2 = x^2, for example. So, a function consisting of only even-degree terms will meet the requirement for an even function. The given f(x) is an even function.

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If f(x) = f(-x), the function reflected across the y-axis is the same as the original function. That is, the y-axis is the axis of symmetry.